# Cool roots.#Pythagorean

**Algebra**Level 5

given that \[ P(x)= x^3 +ax^2 +bx-14760\] has integral roots \(\alpha,\beta,\gamma\) such that \[ \alpha^2 +\beta^2 =\gamma^2\] find\[\] \(P(10)\) \(mod\) \( 88\).\[\] \(details\) & \(assumption\) \[0\ne|\alpha|<|\beta|<|\gamma|, \alpha<\beta<\gamma\] work with the maximum value of \(\alpha,\beta,\gamma\)

All roots are positive.